Question

`int(f'(x))/(sqrt(f(x))) = sqrt(f(x)) + c`

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Let t = f(x). Then, the derivative dt can be expressed in terms of f'(x):

dt = f'(x) dx 

⇒ `dx = dt/(f'(x))`

Substituting t into the integral gives us,

`int (f'(x))/(sqrt(f(x))) dx = int (f'(x))/(sqrt t) * dt/(f'(x))`

= `int 1/(sqrt t) dt`

= `2 sqrt t + c`

= `2 sqrt(f(x)) + c`